The invention relates to a method, implemented within a computer interface, to simplify and enhance the use of numerical simulation tools to design a primary geometry for a powder compact and to design the pressing process used to shape a powder by compaction. More particularly, the invention relates to an interface that utilizes pre-defined generic geometric configurations to simplify the use of finite element method modeling software to more efficiently design the shape and size a powder compact, a forming die to shape a powder compact, and the pressing process used to form a powder compact.
Conventional ceramic component manufacturing often involves processing and fabrication with raw materials in powder form. Granulated powder is formed into a “green” (i.e., not sintered) body of the desired size and shape by consolidation, often by pressing or compacting nominally dry powder in a mold or die (also known as tooling). Ceramic powders are commonly pressed in steel dies or viscoelastic (e.g., rubber) bags with the aim of producing a near-net-shape powder compact for subsequent sintering. Density gradients introduced into a green powder compact during the pressing operation are often severe enough to cause distortions in the shape of the part during sintering due to non-uniform shrinkage. In such cases, extensive and costly machining of the green body, and diamond grinding of the sintered body, can be required to produce a finished part of the desired final shape and size. In severe cases, density gradients and non-uniform shrinkage can create cracks or other performance limiting defects in a finished part after sintering, rendering the part useless. Likewise, severe density gradients can result in powder compacts that break during ejection from the forming die, or that are too fragile to handle during subsequent processing, decreasing manufacturing yields.
Empirical relationships (i.e., rules of thumb) exist to help guide component design and the compaction process used to fabricate powder compacts; however, such relationships do not provide the understanding necessary to control component and die design, and the compaction parameters to eliminate density gradients over a wide variety of design and processing conditions. Consequently, a designer is often must use an expensive and time-consuming trial and error process to develop new components, forming dies, and forming processes. This traditional approach to component design and development is inefficient, expensive, and unreliable. Also, the traditional approach inevitably introduces density gradients of unknown and uncontrolled magnitude during the powder pressing process that contribute to shape distortion, uncontrolled sintering, and ultimately, unpredictable component performance and reliability.
An alternate design and powder processing approach for more efficient ceramic component manufacturing is highly desirable. Particularly, interest has grown in developing and applying computer simulation tools to address this problem. A science-based constitutive materials model can be implemented within a numerical computer simulation tool to aid in the cost-effective design of forming dies and pressing processes to manufacture improved performance and reliability ceramics. A science-based approach provides the insight necessary to control component geometry and the powder compaction process to minimize density gradients in green powder compacts.
Some powder compaction modeling software already exists for metal and ceramic powder processing. Carr and Bono have described compaction modeling software for metal powders (Carr, K. and Bono, E., “PCS Elite™—A Complete Die Compaction Software Package,” Advances in Powder Metallurgy & Particulate Materials—1999: Proceedings of the 1998 International Conference on Powder Metallurgy & Particulate Materials, 3(10–13), Metal Powder Industries Federation; APMI International, 10-111–10-125, 1999). Compaction software for ceramic powders is described by Aydin et al. (Aydin, I., Briscoe, B., and Ozkan, N., “Application of Constitutive Models on Ceramic Powder Compaction via Finite Element Method,” in Diversity Into the Next Century, Proceedings of the 27th International SAMPE Technical Conference, 27, eds. R. J. Martinez, H. Arris, J. A. Emerson, and G. Pike, SAMPE International, Covina, Calif., 590–6, 1995) (Aydin, I., Briscoe, B., and Ozkan, N., “Modeling of Powder Compaction: A Review,” MRS Bulletin, 22[12] 45–51, 1997), and Zipse, (Zipse, H., “Finite-Element Simulation of the Die Pressing and Sintering of a Ceramic Component” J. European Ceram. Soc., 17, [14] 1707–13, 1997).
Realistic predictions of spatial density variations within ceramic powder compact have been made using a cap-plasticity constitutive materials models within an finite element framework by Aydin et al. (Aydin, I., Briscoe, B., and Sanliturk, K., “Density Distributions During the Compaction of Alumina Powders: A Comparison of a Computational Prediction with Experiment,” Comp. Mater. Sci., 3, 55–68, 1994). The generic cap-plasticity constitutive model captures the mechanical behavior of granulated ceramic powder during compaction reasonably well. The cap-plasticity constitutive model is comprised of a stationary shear failure surface and a non-stationary, strain-hardening cap that define the elastic regime for the compaction of a powder in response to both hydrostatic compression and shear, when the second invariant of the deviatoric stress is plotted versus the first invariant of stress. The cap-plasticity constitutive model allows for an initially “small” cap that grows and hardens with increasing pressing pressure during powder compaction, an elastic rebound upon unloading (spring-back), and the possibility for secondary yielding (delamination) if unloading results in an intersection with the shear failure surface.
Compaction modeling tools have been used to simulate powder compaction in two-dimensional and complicated three-dimensional geometry powder compacts. Furthermore, it has been demonstrated that finite element compaction model predictions are accurate enough to be useful design tools in ceramic manufacturing. Compaction modeling has been used to predict shape distortions after pressing by Aydin et al. (Aydin, I., Briscoe. B., Sanliturk. K., 1997, “Dimensional Variation of Die-Pressed Ceramic Green Compacts: Comparison of a Finite Element Modeling with Experiment,” J. European Ceram. Soc., 17, 1201–12.). Additionally, it has been shown that compaction model predictions can be used to guide die designs and pressing processes to minimize density gradients by Keller et al. (Keller, J., French, J., Dinger, B., McDonough, M., Gold, B., Cloutier, C., Carinic, L., Van Horn, E., Ewsuk, K., Blumenthal, B., 1998, “Industry, Government Team to Improve Ceramic Manufacturing,” Bull. Am. Ceram. Soc., 77 [10] 52–7.). Keller et al. described how modeling can provide guidance on the aspect ratios, transition radii, and pressing balance (i.e., the relative displacements of a top and bottom punch in dual-action pressing) to control and minimize density gradients. Zipse (1997) demonstrated that model simulations also can be used to guide die design in combination with green machining to minimize density gradients in the final product. Zipse showed that powder compacts can be formed intentionally oversize such that outer regions with severe density gradients can be physically removed by green machining prior to sintering to net shape.
An appealing aspect of finite element modeling is that realistic and informative simulations of ceramic powder compaction can be completed on simple and relatively complex geometry compacts. Furthermore, simulations can be completed using a workstation, a desktop computer, or even a laptop computer. Additionally, commercial software packages are readily available for finite element modeling.
A general disadvantage of finite element modeling is that reliable and useful simulations are complex, and generally require specialized expertise in computing and mechanics to obtain meaningful results. In particular, constructing the finite element mesh required to run a finite element computer simulation can be extremely time-consuming. Hours to several days can be required to construct suitable mesh inputs.
Traditional methods of generating a finite element mesh for numerical simulations are labor and time intensive. In general, solid mechanics finite element codes have their own mesh generator inherent as part of the input, and are capable of inputting a mesh from an external mesh generator. Older finite element codes can require the input of the nodal numbers and nodal coordinates as well as element number and element connectivity itself, along with a material identification to tag each element's properties before performing finite element calculations (i.e., the entire mesh, material properties, boundary conditions, and initial conditions are defined externally, and input manually). More recent finite element codes generally have a pre-processing tool with which the user defines the geometry to be analyzed, and specifies of how to subdivide that geometry into a finite element mesh. The pre-processing tool requires, as input: points; lines; sides; regions; schemes; element side flags; nodal flags; and body definition. Two or more points define a line; a set of contiguous lines defines a region; and a collection of regions defines a body. Flags are attached to a region to define the properties of that region. Flags are attached to lines and/or sides to define the boundary conditions and/or loading conditions. Lines are subdivided with parameters and increments to generate nodes and elements via the scheme card that is attached to a region. When all of this is done, the mesh with the appropriate flags is then written to a database that is readable by the finite element code. Within the finite element code, the user defines specific boundary conditions (e.g., static and loading conditions) to attach to the flagged element sides and/or nodes, and the corresponding material properties and material behavior corresponding to the flags attached to the different regions. The geometry, material properties, boundary conditions, and initial conditions are provided as input to a deformation, nonlinear, quasi-static, finite element computer program/code, which, when executed, calculates deformation characteristics. The deformation characteristics can then be evaluated to determine the acceptability of the primary geometry and mesh for that geometry, which subsequently be can be modified as deemed necessary to complete a meaningful simulation.
Conventional use of the aforementioned pre-processing finite element tools to define the overall component geometry and build the mesh for a moderately complex part can take several days (e.g., often three to five days) of manual effort. Additionally, effective use of existing numerical modeling software currently requires significant finite element modeling expertise, insight into the underlying mechanics of the compaction process, and experience in using the cap-plasticity constitutive model. Furthermore, constructing the finite element mesh (i.e., computational grid) required to complete the numerical analysis, as well as visualizing results from the database output from the numerical simulation requires additional expertise with several pre- and post-processing tools. These significant requirements and potential impediments for using the underlying software severely limit the application of existing numerical simulation tools by the typical engineer on the production floor.
Broader application of numerical simulation tools and computer-aided component design and powder processing require a more user-friendly tool than the general-purpose, numerical simulation capability currently available. A computer interface that allows a novice with minimal training to more easily define the component geometry, construct the finite element mesh, set-up the numerical simulation, complete the analysis, and visualize the results would significantly enhance the utility of numerical simulation software in the manufacturing environment. In particular, user-friendly software to address component geometry variability without having to manually construct complicated finite element meshes from scratch would significantly enhance the value and utility of numerical simulation tools to the novice user.